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Instructor: Vincent Duffy, Ph.D. Associate Professor of IE Lab 2 Tutorial – Uncertainty in Decision Making Fri. Feb. 2, 2006 IE 486 Work Analysis & Design II

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Today – IE 486 Lab 2 tutorial Discussion on uncertainty in decision making – related to economic decision making and material from ch.7 in Wickens on Decision making in the context of human factors and ergonomics. In lab exercise: Suppose the range of outcomes is known, but the probability distribution is unknown (uncertain). Use a sheet of paper to illustrate the selection of alternative A, B or C based on four different analytical criteria known as Maxi-min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on your sheet of paper and re-calculate to decide based on each of the four criteria.

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Lab 2 Exercise: Decision Making & Uncertainty. Suppose the range of outcomes is known, but the probability distribution is unknown (uncertain). Use a sheet of paper to illustrate the selection of alternative A, B or C based on four different analytical criteria known as Maxi- min, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on your sheet of paper and re-calculate to decide based on each of the four criteria. Observed outcomes of four trials are shown in the payoff matrix below. For each method, determine the expected outcomes before making your decision. What is illustrated by the use of the different analytical techniques? observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 A 6 0 1 3 B 2 4 4 1 B 2 4 4 1 C 0 1 3 8 C 0 1 3 8 1. Maxi-min criteria - pessimistic view try to maximize the minimum outcome a. for any given alternative (eg. A,B, or C), assume the worst possible outcome. b. choose the best (of those previously chosen). 2. Maxi-max criteria - optimistic view try to maximize the maximum outcome a. for any given alternative (eg. A,B, or C), assume the best possible outcome. b. choose the best (of those previously chosen). 3. Mini-max regret criteria –Mini-max Regret: minimize the maximum possible regret. –regret: difference between observed and best payoff. 4. Equal-likelihood criteria a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely. b. maximize the expected value.

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from Chapter 4 in Babcock in Managing Engineering and Technology (Babcock, 1991). –especially... Decision making under uncertainty. p. 74-75 (today) –In Babcock, D.L. 1991. Managing engineering and technology: an introduction to management for engineers, Prentice-Hall: Englewood Cliffs, NJ. You may consider ‘economic’ decision making (related to decisions made on investment alternatives) somewhat different from ‘cognitive’ considerations in decision making (related to decisions made during a task) from the Wickens text. However, this material may be considered to help bridge the material without considering ‘time value of money’ yet. Analytical tools for decision making under uncertainty

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Uncertainty - example 1 In a discussion of forecasting, and decision making –Suppose the range of outcomes is known, but the probability distribution is unknown (uncertain). 1. Maxi-min criteria - pessimistic view –try to maximize the minimum outcome –a. for any given alternative (eg. A,B, or C), assume the worst possible outcome. –b. choose the best (of those previously chosen).

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Uncertainty - example 1 In a discussion of forecasting, and decision making Suppose the range of outcomes is known, but the probability distribution is unknown (uncertain). 1. Maxi-min criteria - pessimistic view try to maximize the minimum outcome a. for any given alternative (eg. A,B, or C), assume the worst possible outcome. b. choose the best (of those previously chosen). Example 1) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 A 6 0 1 3 B 2 4 4 1 B 2 4 4 1 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 1 In a discussion of forecasting, and decision making Suppose the range of outcomes is known, but the probability distribution is unknown (uncertain). 1. Maxi-min criteria - pessimistic view try to maximize the minimum outcome a. for any given alternative (eg. A,B, or C), assume the worst possible outcome. b. choose the best (of those previously chosen). Example 1) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 0 A 6 0 1 3 0 B 2 4 4 1 B 2 4 4 1 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 1 1. Maxi-min criteria - pessimistic view try to maximize the minimum outcome a. for any given alternative (eg. A,B, or C), assume the worst possible outcome. b. choose the best (of those previously chosen). Example 1) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 0 A 6 0 1 3 0 B 2 4 4 1 1 B 2 4 4 1 1 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 1 1. Maxi-min criteria - pessimistic view try to maximize the minimum outcome a. for any given alternative (eg. A,B, or C), assume the worst possible outcome. b. choose the best (of those previously chosen). Example 1) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 0 A 6 0 1 3 0 B 2 4 4 1 1 B 2 4 4 1 1 C 0 1 3 8 0 C 0 1 3 8 0 for maxi-min criteria: choose B

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Uncertainty - example 2 2. Maxi-max criteria - optimistic view try to maximize the maximum outcome a. for any given alternative (eg. A,B, or C), assume the best possible outcome. b. choose the best (of those previously chosen).

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Uncertainty - example 2 2. Maxi-max criteria - optimistic view try to maximize the maximum outcome a. for any given alternative (eg. A,B, or C), assume the best possible outcome. b. choose the best (of those previously chosen). Example 2) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 A 6 0 1 3 B 2 4 4 1 B 2 4 4 1 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 2 2. Maxi-max criteria - optimistic view try to maximize the maximum outcome a. for any given alternative (eg. A,B, or C), assume the best possible outcome. b. choose the best (of those previously chosen). Example 2) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 6 A 6 0 1 3 6 B2 4 4 1 B2 4 4 1 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 2 2. Maxi-max criteria - optimistic view try to maximize the maximum outcome a. for any given alternative (eg. A,B, or C), assume the best possible outcome. b. choose the best (of those previously chosen). Example 2) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 6 A 6 0 1 3 6 B 2 4 4 1 4 B 2 4 4 1 4 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 2 2. Maxi-max criteria - optimistic view try to maximize the maximum outcome a. for any given alternative (eg. A,B, or C), assume the best possible outcome. b. choose the best (of those previously chosen). Example 2) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 6 A 6 0 1 3 6 B 2 4 4 1 4 B 2 4 4 1 4 C 0 1 3 8 8 C 0 1 3 8 8 for maxi-max criteria: choose C

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Uncertainty - example 3 3. Mini-max regret criteria –Mini-max Regret: minimize the maximum possible regret. –regret: difference between observed and best payoff. eg. suppose we chose B, but in outcome 1, if we had chosen A we could have had 6 (from A) instead of 2 (from B). So we have regret…if only we had chosen A, we could have had 4 more!

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Uncertainty - example 3 3. Mini-max regret criteria Mini-max Regret: minimize the maximum possible regret. regret: difference between observed and best payoff. Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcome alternative___1___2___3___4____ _______ _1 2 3 4___max___ A 6 0 1 3 A A 6 0 1 3 A B 2 4 4 1 B B 2 4 4 1 B C 0 1 3 8 C C 0 1 3 8 C for mini-max regret criteria: *choose A

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Uncertainty - example 3 3. Mini-max regret criteria eg. suppose we chose B, but in outcome 1, if we had chosen A we could have had 6 (from A) instead of 2 (from B). So we have regret…if only we had chosen A, we could have had 4 more! Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcome alternative___1___2___3___4____ ______ _ _1 2 3 4___max___ A 6 0 1 3 A 0 A 6 0 1 3 A 0 B 2 4 4 1 B 4 B 2 4 4 1 B 4 C 0 1 3 8 C 6 C 0 1 3 8 C 6

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Uncertainty - example 3 3. Mini-max regret criteria eg. suppose we chose B, but in outcome 1, if we had chosen A we could have had 6 (from A) instead of 2 (from B). So we have regret…if only we had chosen A, we could have had 4 more! Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcome alternative___1___2___3___4____ ______ _ _1 2 3 4___max___ A 6 0 1 3 A 0 A 6 0 1 3 A 0 B 2 4 4 1 B 4 B 2 4 4 1 B 4 C 0 1 3 8 C 6 C 0 1 3 8 C 6

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Uncertainty - example 3 3. Mini-max regret criteria Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcome alternative___1___2___3___4__________ _ _1 2 3 4___max___ A 6 0 1 3 A 0 4 A 6 0 1 3 A 0 4 B 2 4 4 1 B 4 0 B 2 4 4 1 B 4 0 C 0 1 3 8 C 6 3 C 0 1 3 8 C 6 3

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Uncertainty - example 3 3. Mini-max regret criteria Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcome alternative___1___2___3___4____ __________ _1 2 3 4___max___ A 6 0 1 3 A 0 4 3 A 6 0 1 3 A 0 4 3 B 2 4 4 1 B 4 0 0 B 2 4 4 1 B 4 0 0 C 0 1 3 8 C 6 3 1 C 0 1 3 8 C 6 3 1

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Uncertainty - example 3 3. Mini-max regret criteria Example 3) Suppose we have a payoff matrix (payoff) observed outcome (regret matrix) observed outcome alternative___1___2___3___4____ __________ __1 2 3 4___max___ A 6 0 1 3 A 0 4 3 5 5 A 6 0 1 3 A 0 4 3 5 5 B 2 4 4 1 B 4 0 0 7 7 C 0 1 3 8 C 6 3 1 0 6 B 2 4 4 1 B 4 0 0 7 7 C 0 1 3 8 C 6 3 1 0 6 for mini-max regret criteria: choose A

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Uncertainty - example 4 4. Equal-likelihood criteria –this looks more like a ‘risk’ problem because you do use ‘assumed’ probabilities a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely. b. maximize the expected value.

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Uncertainty - example 4 4. Equal-likelihood criteria a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely. b. maximize the expected value. Example 4) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 (6+0+1+3)/4 = 10/4 A 6 0 1 3 (6+0+1+3)/4 = 10/4 B 2 4 4 1 B 2 4 4 1 C 0 1 3 8 C 0 1 3 8

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Uncertainty - example 4 4. Equal-likelihood criteria Example 4) Suppose we have the following payoff matrix observed outcome expected observed outcome expected alternative___1___2___3___4____ outcome ______ A 6 0 1 3 (6+0+1+3)/4 = 10/4 A 6 0 1 3 (6+0+1+3)/4 = 10/4 B 2 4 4 1 (2+4+4+1)/4 = 11/4 B 2 4 4 1 (2+4+4+1)/4 = 11/4 C 0 1 3 8 (0+1+3+8)/4 = 12/4 C 0 1 3 8 (0+1+3+8)/4 = 12/4 for maxi-max criteria: choose C

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